Brillouin–Wigner perturbation theory

E33422

Brillouin–Wigner perturbation theory is a formulation of quantum mechanical perturbation theory that uses an energy-dependent effective Hamiltonian to obtain improved approximations to eigenvalues and eigenstates.

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Predicate Object
instanceOf perturbation theory
quantum mechanical formalism
advantage can improve convergence of perturbation series in some problems
aimsTo obtain improved approximations to eigenstates
obtain improved approximations to eigenvalues
appliedIn nuclear shell-model calculations
appliesTo discrete spectra
time-independent Hamiltonians
assumes existence of a solvable unperturbed Hamiltonian
basedOn partition of Hamiltonian into unperturbed and perturbation parts
category approximation method in quantum theory
characteristic energy appearing on both sides of the eigenvalue equation
comparedTo Rayleigh–Schrödinger perturbation theory
contrastWith Rayleigh–Schrödinger perturbation theory using energy-independent effective Hamiltonian
developedIn 20th century
feature nonlinear dependence of energy corrections on the exact energy
field quantum mechanics
focusesOn corrections to eigenvalues and eigenvectors of the unperturbed Hamiltonian
formalismType time-independent perturbation theory
framework Hilbert space of quantum states
goal improve accuracy beyond low-order perturbation results
involves projection operators onto model space and complementary space
limitation leads to implicit equations for energies
requires self-consistent solution for eigenvalues
mathematicalForm series expansion in powers of the perturbation
namedAfter Eugene Wigner
Léon Brillouin
relatedConcept Brillouin–Wigner perturbation theory self-linksurface differs
surface form: Brillouin–Wigner expansion

Brillouin–Wigner perturbation theory self-linksurface differs
surface form: quasi-degenerate perturbation theory
relatedTo Feshbach projection formalism
effective Hamiltonian methods
requires choice of model space
definition of projection operators
usedFor bound-state problems in quantum mechanics
many-body quantum systems
usedIn atomic physics
condensed matter physics
molecular physics
usedToDerive effective interactions in model spaces
uses energy-dependent effective Hamiltonian
yields energy-dependent effective Hamiltonian in model space

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Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Rayleigh–Schrödinger perturbation theory relatedTo Brillouin–Wigner perturbation theory
Brillouin–Wigner perturbation theory relatedConcept Brillouin–Wigner perturbation theory self-linksurface differs
this entity surface form: quasi-degenerate perturbation theory
Brillouin–Wigner perturbation theory relatedConcept Brillouin–Wigner perturbation theory self-linksurface differs
this entity surface form: Brillouin–Wigner expansion
Léon Brillouin notableConcept Brillouin–Wigner perturbation theory